A M E RI C A N E N TE R P R I S E IN S T I T U TE 1
n 2012, two of us (Hassett and Veuger)
performed a statistical analysis of injury
data and investigated whether that data
supported the contention that New Orleans
Saints players were statistically more likely to
injure opponents than players on other teams.
We found that, in fact, the Saints players injured
fewer competing players than all but one team
during the first year of their supposed “bounty”
program, and that there was no evidence over the
entire period that the Saints injured more players
than the typical team. Following our testimony
before former National Football League (NFL)
Commissioner Paul Tagliabue, the NFL’s
penalties against the Saints players were
withdrawn, and news accounts have pointed to
our analysis as contributing to that decision.
In the current “Deflategate” controversy in which
the New England Patriots have been accused of
illicitly deflating footballs before the start of the
2015 American Football Conference
championship game, the NFL and lawyers it hired
have produced a report that has been used to
justify penalties against the Patriots and,
specifically, Tom Brady (Wells Jr., Karp, and
Reisner 2015).1 The Patriots received a $1 million
fine and lost two draft picks, which the team
declined to appeal (Jones 2015). The NFL Players
Association (NFLPA) has appealed Tom Brady’s
suspension and criticized the report as biased
(Jones 2015). For example, NFLPA Executive
1 Hereinafter, we refer to the report as the “Wells report,” its colloquial referent.
June 2015
On the Wells report
By Kevin A. Hassett, Joseph W. Sullivan, and Stan A. Veuger
I
In the current “Deflategate” controversy, the New England Patriots have been accused of illicitly deflating footballs before
the start of their 2015 American Football Conference championship game against the Indianapolis Colts. The National
Football League and the lawyers it hired have produced a report—commonly known as the “Wells report”—that has been
used to justify penalties against the Patriots and quarterback Tom Brady. Although the Wells report finds that the Patriots
footballs declined in pressure significantly more than the Colts balls in the first half of the game, our replication of the
report’s analysis finds that it relies on an unorthodox statistical procedure at odds with the methodology the report
describes. It also fails to investigate all relevant scenarios. In addition, it focuses only on the difference between the Colts
and Patriots pressure drops. Such a difference, however, can be caused either by the pressure in the Patriots balls
dropping below their expected value or by the pressure in the Colts balls rising above their expected value. The second of
these two scenarios seems more likely based on the absolute pressure measurements. Logistically, the greater change in
pressure in the Patriots footballs can be explained by the fact that sufficient time may have passed between halftime
testing of the two teams’ balls for the Colts balls to warm significantly, effectively inflating them.
A M E RI C A N E N TE R P R I S E IN S T I T U TE 2
Director DeMaurice Smith said the report
“delivered exactly what the client wanted” (CBS
Boston 2015). On the other hand, the experts
employed by the NFL have solid credentials and
deserved reputations.
Given that our impartiality was in the past at least
implicitly recognized by the NFL and
Commissioner Tagliabue, we believe we are a
uniquely qualified third party to evaluate the
merits of the evidence provided in the Wells
report. In this paper, we review the Wells report,
attempt to replicate its statistical analysis, and
explore its possible shortcomings.
Our findings are as follows. First, the Wells report
contains sufficient data to explore the question of
whether the Patriots deflated their footballs using
statistical techniques. Second, the Wells report’s
statistical analysis cannot be replicated by
performing the analysis as described in the
report. Third, the Wells report’s results can (for
the most part) be replicated when we use a
different, flawed modeling approach that
fundamentally differs from the approach
described in the report. Fourth, the Wells report
failed to recognize the importance of the logical
link between two of its areas of inquiry: whether
the Patriots balls were deflated more than the
Colts balls, and whether the Patriots balls were at
a pressure that could be explained without
recourse to wrongdoing by the Patriots.
When correct tests are performed, the evidence
points to a conclusion that is inconsistent with
the Wells findings. Our evidence suggests a
specific sequence of events. The Wells report
conclusions are likely incorrect, and a simple
misunderstanding appears to have led the NFL to
these incorrect conclusions.
Did the Patriots Balls Experience
a Larger Pressure Drop Than the
Colts Balls?
In this section, we begin by replicating the Wells
analysis. Then, we discuss the dependence of the
analysis on assumptions concerning which
pressure gauges were used. Finally, we provide a
thorough analysis of all the possible permutations
of measurement-device combinations.
Replicating the Core Wells Analysis
The core contribution of the Wells report is a
statistical analysis that appears to demonstrate
that the Patriots balls exhibited a greater pressure
decline between the pregame and halftime
pressure measurements than the Colts balls. In
this section, we review the authors’ methodology
and attempt to replicate their findings. We find,
as the Wells report did, that the evidence suggests
on balance that the Patriots balls declined in
pressure more than the Colts balls under the
maintained assumptions in the report. As we will
explain, however, this does not necessarily
constitute evidence that the Patriots illegally
tampered with their footballs.
From the report, a clear picture of the ball
measurement process emerges. Referee Walt
Anderson measured the pressure of the balls
before the game at 12.5 pounds per square inch
(PSI) for the Patriots and 13.0 or 13.1 PSI for the
Colts (Wells Jr., Karp, and Reisner 2015, 52).
During halftime, Clete Blakeman and Dyrol
Prioleau, alternative referees, measured the
pressure of 11 balls from the Patriots and 4 balls
from the Colts. At least one of the gauges used
was the same gauge Anderson used before the
game. Blakeman and Prioleau could measure only
four of the Colts balls because they were nearing
the end of halftime and needed the balls for the
game (Wells Jr., Karp, and Reisner 2015, 7; 69).
Perhaps the most important contribution the
report purports to make lies in its analysis of
these data. After all, if the rigor of statistical
analysis supports the claim that the Patriots
illegally deflated their footballs, this would
constitute strong evidence of wrongdoing on their
part. The Wells report describes its approach as
follows: The statistical model that serves as the
baseline for estimating the effects of the various
variables “expresses the pressure drop associated
with a single halftime measurement as composed
of a series of additive terms” (Wells Jr., Karp, and
Reisner 2015, A-3). More specifically, the report
claims to present estimates derived from the
following equation, which expresses the decrease
in ball pressure for a given ball (ijk) as a function
of a constant term (μ), team-fixed effects (αi),
gauge/official-fixed effects (βj), their interaction,
A M E RI C A N E N TE R P R I S E IN S T I T U TE 3
and two error terms:
This equation suggests that a multiple regression
analysis was performed. But when we estimate
the regression described in the report, the results
are quite different from those reported by the
authors. After some trial and error, though, we
were able to replicate almost all of the results
presented. Table 1 shows the values presented in
Table A-2 in appendix A of appendix 1 on page A-
4 of the Wells report, alongside the results of our
best attempts to replicate them. As one can see,
the estimated effects match perfectly for all of the
listed effects, with the exception of “Gauge.”
The precision with which all but two of our table 1
estimates match those of the Wells report renders
it extraordinarily unlikely that our attempts to
replicate the data presented in table A-2 of the
Wells report used anything but the same analysis
used to generate those values in the report. Yet
the regression specification used to produce these
results—and, presumably, those of the Wells
report—is certainly not a standard specification.
Although the text that prefaces table A-2
indicates that the values are “adjusted for other
effects,” implying the authors performed a
multiple regression, they seem to be the result of
simply including no other explanatory variables
(and excluding a constant term). For instance, the
regression that estimates the “Team effects”
includes no other variable besides “Team.” The
interaction-term effects are estimated from an
equation that includes only the four interaction
terms and specifies the lack of a constant term.
That is, the equations that were actually
estimated appear to be of the following form,
where dy represents a dummy variable for
category y = 1 . . . Y and where Σ sums over 1
through Y:
PSIDrop(team i, gauge/official j, ball k) =
Σ[βydy,ijk] + ϵijk
For instance, in the case of the category of
“Team,” there would be two dummy variables,
dPATRIOTS and dCOLTS. This approach of estimating a
variable’s effect while omitting other variables
produces biased estimates and is at odds with the
description in the report of the approach taken,
which describes an approach that would have
been closer to the norm.
This replication is consistent with the balance of
the Wells results, but not with the report’s
description of its methods. In the next section, we
show results for an appropriate analysis of the
data that roughly confirms the Wells results on
the relative pressure decline but contradicts it in
a crucial way.
Table 1. Replicating the Wells Report
Effect Team Gauge Wells values Replicated values
Team Colts #N/A -0.469 -0.4687
Team Patriots #N/A -1.202 -1.2022
Gauge #N/A A -0.883 -1.12
Gauge #N/A B -0.788 -0.8933
Team*Gauge Colts A -0.375 -0.375
Team*Gauge Colts B -0.563 -0.5625
Team*Gauge Patriots A -1.391 -1.3909
Team*Gauge Patriots B -1.014 -1.0136
Notes: This table reports, in the right-most column, the authors’ best attempt to replicate the coefficients featured in Table A-2 of the Wells report. To the left of that column are the coefficients featured in the Wells report. The authors generated the replicated values using the equation referenced in the three paragraphs preceding this table rather than the equation the Wells report leaves the impression of having used. The equation the Wells report leaves the impression of having used features a single multivariate regression, yet the equation that replicates most of their results runs each set of variables in a separate regression. Source: Authors’ calculations based on Theodore Wells Jr., Brad S. Karp, and Lorin L. Reisner, Investigative Report Concerning Footballs Used during the AFC Championship Game on January 18, 2015 (Paul, Weiss, Rifkind, Wharton & Garrison LLP, May 6, 2015), http://online.wsj.com/public/resources/documents/Deflategate.pdf.
A M E RI C A N E N TE R P R I S E IN S T I T U TE 4
Two Different Gauges
The Patriots and Colts balls were, according to
Anderson’s best recollection, measured by him at
12.5 and 13.1 PSI, respectively, before the game.
This measurement was the starting point for the
investigation. Anderson had two different
pressure gauges, one that the report refers to as
the “Logo” gauge, as it has a logo on it, and one
referred to as the “Non-Logo” gauge.
At halftime, 11 of the Patriots balls and only 4 of
Colts balls were measured with both gauges.
Unfortunately, the Logo gauge tends to give
higher readings than the Non-Logo gauge (by
about 0.4 PSI), and this has created some
controversy. Anderson remembers that he used
the Logo gauge before the game, but the Wells
report, in a direct contradiction of that
recollection, concludes that he used the Non-
Logo gauge before the game. The Patriots have
argued that this decision was crucial to the
analysis and that the evidence of excessive
deflation disappears if one assumes the Logo
gauge was used. Wells, in a news conference after
the report was released, has stated that his
report’s results continue to hold and that “it
doesn’t matter because regardless of which
gauges were used the scientific consultants
addressed all of the permutations in their
analysis” (Boston Globe 2015).2
This statement is factually incorrect. The Wells
report neither provides evidence for every
possible permutation of gauge use nor proves that
the report’s conclusions are independent of gauge
use. If, as the Wells report asserts, Anderson’s
recollection is unreliable, then it seems to
logically follow that one way to perform a
thorough analysis would be to address all four
possible permutations of gauge use.
Two gauges and two teams implies four possible
permutations of pregame gauge use: (1) the
Patriots balls were measured with the Logo gauge
whereas the Colts balls were measured with the
2 Page 114 of the Wells report makes a claim that is for all intents and purposes synonymous: “According to both Exponent and Dr. Marlow, the difference in the average pressure drops between the Patriots and Colts footballs is statistically significant. The conclusion was consistent regardless of the assumptions made as to which of the two gauges was used to measure the game balls prior to the game and at halftime.”
Non-Logo gauge, (2) the Patriots balls were
measured with the Non-Logo gauge whereas the
Colts balls were measured with the Logo gauge,
(3) both teams’ balls were measured with the
Logo gauge, or (4) both teams’ balls were
measured with the Non-Logo gauge. We analyze
each possibility separately using a standard
statistical model.
Tables 2–5 show the results of statistical analysis
for all four possible permutations. They are
estimates from an equation of the following form,
where µ is a constant, Nk is a count variable for
the order in which ball k was measured, IPatriots is
an indicator variable for whether the ball
belonged to the Patriots, and ϵ is an error term:
PSIDrop(k) = µ + αNk + βIPatriots + ϵk
The variable of primary interest is the coefficient
on the dummy variable for the Patriots, β. If β is
positive and statistically significant, it would
indicate that the drop in pressure of the Patriots
balls between their pregame and halftime
pressure measurements was statistically
distinguishable from the drop in pressure of the
Colts balls between their measurements. If Wells
is correct in asserting that the choice of gauge has
no effect on the outcome of analysis, then β
should be positive and statistically significant at
the 5 percent level in each of the four possible
gauge permutations.3 But as we will see, it is not.
Tables 2–5 show the analysis for each of the four
possible pregame gauge scenarios, with three
different cuts of the data: one with the
observations stacked so that each of the two
measurements of each ball at halftime is treated
as an independent observation, one with the
observations generated by the Logo gauge at
halftime, and one with the observations
generated by the Non-Logo gauge at halftime.4
3 We adopt the 5 percent confidence interval from the Wells report as our significance threshold. As noted on page 11 in the Exponent section of the Wells report, “The convention in statistical applications is to declare a finding significant if the p-value is less than 0.05.” 4 We include specifications that sort each set of halftime observations by gauge because it seems plausible to assume that the distribution of errors would be different for each halftime gauge, and running them in a single regression fails to account for this possibility.
A M E RI C A N E N TE R P R I S E IN S T I T U TE 5
Table 2 shows that, under the assumption that
the Logo gauge was used to measure both teams’
balls before the game, whether the Patriots
variable is significant depends on which cut of the
data is used. The stacked regression and the Non-
Logo gauge regression are significant, whereas
the Logo gauge regression is not.
Table 3 shows that the Patriots variable is not
significant at the 5 percent level in any of the
three specifications if you assume that before the
game the Logo gauge was used to measure the
Patriots balls while the Non-Logo gauge was used
to measure the Colts balls.
Table 4 shows that under the assumption that the
Non-Logo gauge was used to measure the Patriots
balls while the Logo gauge was used to measure
the Colts balls, the Patriots variable is significant
with all three cuts of the data. And table 5 shows
that, under the assumption that the Non-Logo
gauge was used to measure the balls of both
teams before the game as with table 2, the result
is sensitive to which cut of the data is used.
These results, in aggregate, contradict Wells’s
claim that the analysis yields the same result
regardless of which set of assumptions about the
two gauges was used.5 Three of the four runs with
the stacked data suggest that the Patriots balls
5 Running clustered versions of our regressions (in
other words, specifications that allow the standard
errors to be correlated for observations regarding
the same team, gauge, or ball) yields very similar
results to those reported in Tables 2–5.That is not
extraordinarily surprising: even the teams’ balls do
not have statistically significantly different
variances in their pressure levels.
Table 2. Pregame Gauge Assumption: Logo Gauge for Both Teams
Constant Order Patriots
Stacked Coefficient 0.033 0.249 .820**
t-stat (p-value) .09 (.927) 1.02 (.315) 3.46 (.002)
Logo gauge Coefficient 0.205 0.020 0.689
t-stat (p-value) .40 (.693) .57 (.577) 2.02 (.066)
Non-Logo gauge Coefficient -0.14 0.030 0.952*
t-stat (p-value) -.26 (.800) .80 (.436) 2.63 (.022)
Notes: This table shows the coefficients and statistical significance metrics for each of the three variables included in our preferred regression specification: a “Constant” term (the inclusion of which is standard practice), an “Order” variable that numbers the balls 1–15 based on the order in which they were tested, and a “Patriots” dummy variable that has a value of 0 in the case of the Colts and a value of 1 in the case of the Patriots. The “Stacked” set of coefficient and corresponding significance rows show the regression results if you include the observations generated by both the Logo and Non-Logo gauges during the halftime measurement process as separate observations, the two Logo gauge rows below that show the regression output if you include only the 15 observations generated by the Logo gauge during halftime, and the two Non-Logo gauge rows include the regression output if you only include the 15 observations generated by the Non-Logo gauge during halftime. The data used in this specification of the regression assume that the Logo gauge was the gauge that Anderson used to measure the balls of both the Patriots and the Colts before the game. * indicates significance at a 5 percent confidence level; ** indicates significance at a 1 percent confidence level. Source: Authors’ calculations based on Theodore Wells Jr., Brad S. Karp, and Lorin L. Reisner, Investigative Report Concerning Footballs Used during the AFC Championship Game on January 18, 2015 (Paul, Weiss, Rifkind, Wharton & Garrison LLP, May 6, 2015), http://online.wsj.com/public/resources/documents/Deflategate.pdf, A-4.
Table 3. Pregame Gauge Assumption: Logo Only for Patriots
Constant Order Patriots
Stacked Coefficient 0.433 0.025 0.420
t-stat (p-value) 1.23 (.231) 1.02 (.315) 1.77 (.088)
Logo gauge Coefficient 0.605 0.020 0.289
t-stat (p-value) 1.19 (.255) .57 (.577) .85 (.413)
Non-Logo gauge Coefficient 0.260 0.030 0.552
t-stat (p-value) .48 (.637) .80 (.436) 1.53 (.153)
Notes: This table shows the coefficients and statistical significance metrics for the same equation as table 2 does and presents the data in the same way. However, this specification of the regression assumes that Anderson used the Logo gauge for the Patriots and the Non-Logo gauge for the Colts when generating his pregame pressure readings. Source: Authors’ calculations based on Theodore Wells Jr., Brad S. Karp, and Lorin L. Reisner, Investigative Report Concerning Footballs Used during the AFC Championship Game on January 18, 2015 (Paul, Weiss, Rifkind, Wharton & Garrison LLP, May 6, 2015), http://online.wsj.com/public/resources/documents/Deflategate.pdf, A-4.
A M E RI C A N E N TE R P R I S E IN S T I T U TE 6
deflated more than the Colts balls in the first half,
making it “more likely than not” that illegal
tampering occurred—if one assumes a
statistically significant difference between the
pressure drops experienced by each team to
necessarily constitute evidence of illegal
tampering. Yet even this inference is not
independent of assumptions about which gauges
were used when. As noted earlier, this analysis
deals with the Wells report’s assertion that
Anderson’s recollection is unreliable by regarding
all of the four possible gauge-use permutations as
equally likely and therefore granting each of the
four possible permutations equal weight when
formulating an inference based on the
aggregation of the results. But other approaches
are nevertheless possible.
For instance, one might make the assumption
that Anderson used the same gauge to measure
both the Colts and Patriots footballs before the
game, but still remain uncertain as to which of
the two gauges that single gauge was. In such a
case, the results would be statistically significant
in the specification that analyzes the stacked
observations from both gauges at halftime and in
the specification that analyzes only the
observations generated by the Non-Logo gauge at
halftime, but not in the specification that analyzes
only the observations generated by the Logo
gauge at halftime. Again, this would seem to be
Table 4. Pregame Gauge Assumption: Logo Only for Colts
Constant Order Patriots
Stacked Coefficient 0.033 0.025 1.220**
t-stat (p-value) .09 (.927) 1.02 (.315) 5.14 (.000)
Logo gauge Coefficient 0.205 0.020 1.089**
t-stat (p-value) .40 (.693) .57 (.577) 3.20 (.008)
Non-Logo gauge Coefficient -0.140 0.030 1.352**
t-stat (p-value) -.26 (.800) .80 (.436) 3.74 (.003)
Notes: This table shows the coefficients and statistical significance metrics for the same equation as table 2 does and presents the data in the same way. However, this specification of the regression assumes that Anderson used the Logo gauge for the Colts and the Non-Logo gauge for the Patriots when generating his pregame pressure readings. * indicates significance at a 5 percent confidence level; ** indicates significance at a 1 percent confidence level. Source: Authors’ calculations based on Theodore Wells Jr., Brad S. Karp, and Lorin L. Reisner, Investigative Report Concerning Footballs Used during the AFC Championship Game on January 18, 2015 (Paul, Weiss, Rifkind, Wharton & Garrison LLP, May 6, 2015), http://online.wsj.com/public/resources/documents/Deflategate.pdf, A-4.
Table 5. Pregame Gauge Assumption: Non-Logo for Both Teams
Constant Order Patriots
Stacked Coefficient 0.433 0.025 0.820**
t-stat (p-value) 1.23 (.231) 1.02 (.315) 3.46 (.002)
Logo gauge Coefficient 0.605 0.020 0.689
t-stat (p-value) 1.19 (.255) .57 (.577) 2.02 (0.066)
Non-Logo gauge Coefficient 0.260 0.030 0.952*
t-stat (p-value) .48 (.637) .80 (.436) 2.63 (.022)
Notes: This table shows the coefficients and statistical significance metrics for the same equation as table 2 does and presents the data in the same way. However, this specification of the regression assumes that Anderson used the Non-Logo gauge for the Patriots and the Colts when generating his pregame pressure readings. * indicates significance at a 5 percent confidence level; ** indicates significance at a 1 percent confidence level. Source: Authors’ calculations based on Theodore Wells Jr., Brad S. Karp, and Lorin L. Reisner, Investigative Report Concerning Footballs Used during the AFC Championship Game on January 18, 2015 (Paul, Weiss, Rifkind, Wharton & Garrison LLP, May 6, 2015), http://online.wsj.com/public/resources/documents/Deflategate.pdf, A-4.
A M E RI C A N E N TE R P R I S E IN S T I T U TE 7
evidence that lends credence to the claim that
illegal tampering of the balls occurred—if one
assumes a statistically significant difference
between the pressure drops experienced by each
team to necessarily constitute evidence of illegal
tampering.
However, even an unequivocal finding of a
statistically significant difference between the
pressure drops of the Patriots and of the Colts
does not necessarily constitute evidence of illegal
deflation. We explain why in the next section.
Can Ambient Temperature
Changes Explain the Pressure
Difference between the
Patriots and Colts Balls?
The pressure of a football depends on the
ambient temperature of the atmosphere in which
it is located. Footballs inflated to 12.5 PSI at room
temperature will drop in pressure when taken
into the cold. The pressure in the football will
increase when it is brought back into a warm
room. Estimating how much the pressure in the
ball will decline when the external temperature
changes involves straightforward physics.
An investigation that identifies wrongdoing on
the part of the Patriots should document three
things: that the pressure in the Patriots balls
declined more than the pressure in the Colts
balls, that the pressure in the Patriots balls was
significantly below the level predicted by basic
physics, and that the pressure in the Colts balls
was not statistically above or below the level
predicted by basic physics. The confluence of
these three results would represent a smoking
gun. However, the statistically different reduction
in pressure could result either because the
Patriots balls declined more than predicted or
because the Colts balls declined less than
predicted. The Wells report provides no statistical
analysis on this key point.
The problem here is that ideally, measurements
would have been taken simultaneously for all
balls, outdoors, at the end of the half, and with
the same gauge that was used before the game.
Instead, the balls were taken inside and measured
there, but not measured simultaneously. The
pressure was checked twice for the Patriots balls
(once with each gauge), after which the Patriots
balls were reinflated and the Colts ball pressure
was measured. Only 4 of the Colts balls (instead
of all 12) were measured because halftime ended
and the officials ran out of time. The fact that the
officials ran out of time is highly material: it
implies that the Colts balls were inside a warm
room for almost the entire halftime before they
were measured and thus had a chance to warm
up.
The Wells report’s analysis focuses on the
pressure drop of the Patriots balls between their
pregame and halftime measurements relative to
the pressure drop of the Colts balls between their
pregame and halftime measurements. The
question the report attempts to answer is whether
the pressure drop of the Patriots balls can be
explained as the natural pressure drop of a
football used during the game, or whether only
human intervention can explain the pressure
reduction.
Fortunately, the Wells report provides sufficient
data to test this. First, it specifies the range of
pressures that the Ideal Gas Law suggests the
balls could have read given the temperature
change from indoors to outdoors. That range,
according to the report, is 11.32 to 11.52 in the
case of the Patriots and 11.80 to 12.00 in the case
of the Colts (Wells Jr., Karp, and Reisner 2015).
Again, as there is uncertainty concerning which
gauge was used before the game, we explore all
four possible permutations.
The Wells report also documents that the
temperature of the surrounding environment
influences the internal pressure of a football even
over very short time intervals. The report notes,
for instance, that the 0.7 PSI impact on a football
of “vigorous rubbing” dissipates after a window of
roughly 15–30 minutes. And a chart on page 31 of
the Exponent section of the Wells report shows
pronounced effects of air temperature on ball
pressure in a span of what appears to be roughly
15 minutes (Wells Jr., Karp, and Reisner 2015,
31).
The report also notes that halftime was scheduled
to last 13 minutes and that the Colts balls were
measured toward the very end of that window,
when they ran out of time. We can therefore infer
A M E RI C A N E N TE R P R I S E IN S T I T U TE 8
that the Colts balls were tested after being
indoors for a period of a bit less than 15 minutes.
The first of the Patriots balls was measured right
at the beginning of halftime, followed by the
others.
The differences in the pressure drop of each
team’s balls between pregame and halftime that
are documented by the Wells report can be
explained by this difference in the timing of
measurements. Tables 6 and 7 report the results
of a t-test for whether the pressure of the balls
measured at halftime is statistically
distinguishable from the bottom of the range
predicted for the beginning of based on the Ideal
Gas Law.6 In principle, one could take into
account the duration of exposure to the ambient
temperature of the Officials’ Locker Room, where
the halftime testing occurred, when forming a
benchmark for what the pressure of the each
team’s balls should measure if there were no
illegal tampering.
Yet the officials’ failure to record the precise time
at which the balls were tested during halftime
6 Note that because the starting pressure of the football is a variable in calculating the pressure according to the Ideal Gas Law, it is necessary to make an adjustment to the Ideal Gas Law range stated in the Wells report for cases in which the low gauge was used as the starting gauge. The Ideal Gas Law range is a linear function of the starting pressure: if the starting pressure were 0.4 lower than the 12.5 starting value observed, then the Ideal Gas Law range minimum value should be lower by a factor 12.1 divided by 12.5, since the Wells report calculates the range based on the assumption that the starting pressure was 12.5 and the Ideal Gas Law is a linear function of the starting pressure. However, this adjustment has no effect on the main results: it effectively turns the values displayed for the low pregame gauge assumption into the values that correspond to the high pregame gauge assumption for a given halftime gauge assumption (i.e., the right and left sides of tables 6 and 7 would display the same results displayed on the left side of tables 6 and 7). The only effect is thus to remove the one result that is positive and significant for the Patriots.
precludes the possibility of making precise
adjustments for the expected pressure of the balls
based on their exposure to the room’s ambient
temperature. The values shown in tables 6 and 7
are the average distance from the bottom of that
range; a negative value indicates that it is below
the value implied by the Ideal Gas Law. Separate
tests are run for the observations generated by
each of the two gauges at halftime, and results are
reported for both possible pregame gauges.
As table 6 shows, the Patriots balls do not
significantly deviate from the prediction of the
Ideal Gas Law in the direction that one would
expect based on the Wells report’s conclusions
and the NFL’s disciplinary measures. The only
significant result, in fact, indicates that the
Patriots balls were more inflated than the Ideal
Gas Law would imply.
By contrast, as shown in table 7, all the results for
the Colts are statistically significant at the 5
percent level and are higher than the bottom of
the range implied by the Ideal Gas Law for all
possible gauge combinations.
The difference between the Patriots pressure drop
and the Colts pressure drop, then, is significant,
but only because the Colts ball pressure dropped
too little rather than because the Patriots ball
pressure dropped too much. This can be fully
explained by the order in which they were tested.
When the Colts balls were sitting in the room,
estimated by the Wells report to be between 71
and 74 degrees Fahrenheit, for much of the
duration of the 13-minute halftime, their pressure
rose (Wells Jr., Karp, and Reisner 2015, XII). The
Patriots balls, by contrast, were tested earlier on.
Note that this situation is observationally
distinguishable from a situation in which the
Table 6. The Patriots Balls at Halftime
Pregame gauge
Halftime gauge
High Low
High 0.166 .528**
Low -0.211 0.151
Notes: This table shows the average distance of the halftime measurements of the Patriots balls from the bottom of the range implied by the Ideal Gas Law for each of the four possible permutations of pregame and halftime gauges. ** indicates significance at a 1 percent confidence level. Source: Authors’ calculations based on Theodore Wells Jr., Brad S. Karp, and Lorin L. Reisner, Investigative Report Concerning Footballs Used during the AFC Championship Game on January 18, 2015 (Paul, Weiss, Rifkind, Wharton & Garrison LLP, May 6, 2015), http://online.wsj.com/public/resources/documents/Deflategate.pdf, A-4.
A M E RI C A N E N TE R P R I S E IN S T I T U TE 9
difference in pressure drops can be explained by
the Patriots illegally deflating their balls. In such
a scenario, you would expect the Patriots balls to
measure statistically significantly below the
bottom of the range implied by the Ideal Gas Law.
You would also expect the Colts ball pressure to
not be statistically significantly different from the
bottom of the range implied by the Ideal Gas Law.
But the Patriots difference is not significant and
the Colts difference is significantly above the
implication of the Ideal Gas Law. This pattern is
wholly inconsistent with the conclusions of the
Wells report.7
An additional piece of statistical evidence also
points to the scenario in which there was a non-
negligible period of time between the end of the
halftime measurement of the Patriots balls and
the start of the halftime measurement of the Colts
balls. The coefficient on the count variable for the
order in which the balls were tested in our
regression (Nk) varies in precisely the way that
one would expect to observe if the individual
Patriots balls were tested in rapid succession, and
the individual Colts balls were tested in rapid
succession, while the start of the testing of the
Colts balls did not follow immediately after the
end of the testing of the Patriots balls.
You would expect the order variable to be
significant in the regression only when the team
variable is excluded, since variation in pressure
drop arising from the order of testing would be
arising as a consequence of variation in team.
This is what the data reveal: in three of the four
7 The data are also consistent with the hypothesis that the Colts illegally inflated their footballs. But different durations of premeasurement exposure to the temperature of the locker room provide a more parsimonious explanation.
possible permutations using the stacked data, the
regression term for the order in which the balls
were tested becomes significant if you exclude the
team dummy variable but is insignificant if you
include the team dummy variable.
The referees’ apparent switching of gauges
between the halftime testing of the Patriots
footballs and the halftime testing of the Colts
footballs further points to the specific scenario of
a non-negligible duration of time elapsing
between the end of the testing of the Patriots balls
and the start of the testing of the Colts balls
(Wells Jr., Karp, and Reisner 2015, 69; 116–17).
That is, one inference central to the report’s
conclusion is that the alternative referees,
Blakeman and Prioleau, switched gauges between
the measurement of the Patriots and Colts balls.
Specifically, according to the report, during
halftime Prioleau most likely used the Logo gauge
to test the Patriots balls and the Non-Logo gauge
to test the Colts balls, and Blakeman most likely
used the Non-Logo gauge to test the Patriots balls
and the Logo gauge to test the Colts balls (Wells
Jr., Karp, and Reisner 2015, 69; 116–17). This
switching of the gauges was deduced from the
observation that Prioleau registered consistently
higher pressure readings for the Patriots, while
Blakeman registered consistently higher readings
for the Colts. No one present at the time seems to
have noticed any switching of the gauges (Wells
Jr., Karp, and Reisner 2015, 69).8 Absent a non-
8 The Wells report makes clear that this switch became apparent only ex post facto, rather than contemporaneously to the individuals being present. According to the Wells report: “For the reasons stated in Section VII.B and described in detail in Appendix 1, based on Exponent’s conclusion that the Logo Gauge generally reports a measurement that is approximately 0.3-0.45 PSI higher than the measurement reported by the Non-Logo Gauge and never produced a reading lower than the
Table 7. The Colts Balls at Halftime
Pregame gauge
Halftime gauge
High Low
High .825** 1.18**
Low .6375* 1.00*
Notes: This table shows the average distance of the halftime measurements of the Colts balls from the bottom of the range implied by the Ideal
Gas Law for each of the four possible permutations of pregame and halftime gauges. * indicates significance at a 5 percent confidence level; ** indicates significance at a 1 percent confidence level. Source: Authors’ calculations based on Theodore Wells Jr., Brad S. Karp, and Lorin L. Reisner, Investigative Report Concerning Footballs Used during the AFC Championship Game on January 18, 2015 (Paul, Weiss, Rifkind, Wharton & Garrison LLP, May 6, 2015), http://online.wsj.com/public/resources/documents/Deflategate.pdf, A-4.
A M E RI C A N E N TE R P R I S E IN S T I T U TE 1 0
negligible duration of time between the end of the
testing of Patriots balls and the beginning of
testing of the Colts, this unbeknownst switching
of the gauges would appear anomalous, if not
puzzling.
After all, it becomes easy to imagine how
Blakeman and Prioleau switched gauges if a non-
negligible length of time passed between the
testing of the Patriots and the testing of the Colts
balls. On the other hand, if they had started
measuring the Colts footballs immediately after
they completed measuring the Patriots footballs,
it would be more difficult to imagine how or why
they would have switched gauges, let alone done
so without anyone at the time apparently noticing
the gauge switch.
A crucial piece of evidence supporting this
scenario was overlooked in the report’s analysis.
The Colts intercepted a Patriots ball during the
first half, and Colts staff thought it felt
underinflated. Its pressure was then tested
separately from the other 11 Patriots balls. This
separate round of testing offers a data point in a
setting other than the setting in which the
remaining 11 balls were tested. Assuming that the
intercepted Patriots ball that was tested was
inflated to 12.5 PSI before the game, the average
of three measurements derived by this separate
measurement process (11.52 PSI) was at the top
of the range implied by the Ideal Gas Law,
according to the Wells report.9
We can quantify how likely it would be for this to
occur if we take the conclusions of the Wells
report as our null hypothesis. Although the Wells
report does not explicitly specify a quantity that
the Patriots attempted to deflate the footballs by,
the language of the report leaves one with the
impression that its authors had in mind a range
of 0.45 PSI to 1.02 PSI (Wells Jr., Karp, and
Reisner 2015, 114; 9–10).10 Thus, one could
Non-Logo Gauge during Exponent’s testing, it appears most likely that the two officials switched gauges in between measuring each team’s footballs, meaning that Blakeman most likely used the Logo Gauge and Prioleau most likely used the Non-Logo Gauge to test the Colts balls at halftime.” 9 If the Patriots deflated all of their balls measured at halftime except for this one, the odds that the Colts would intercept the clean ball would of course only be 1 in 12, or 8.3 percent. There is no evidence for this having occurred. 10 According to the report, “When compared to the reported pre-game pressures of 12.5 PSI and 13.0 PSI, respectively, the average pressure drop of the Patriots game balls exceeded the
regard deflation of 0.45 PSI as the low-end
estimate and about 1.0 PSI as the high-end
estimate of the extent to which human-induced
deflation occurred.
Suppose one accepts the Wells report assumption
that the Non-Logo gauge was used to generate the
12.5 PSI reading before the game. If one also
accepts the low end of the range implied in the
Wells report—that the Patriots balls had been
deflated by about 0.45 PSI—then the intercepted
ball should have measured between 11.32 PSI −
0.45 PSI (i.e., 10.87 PSI) and 11.52 PSI − 0.45 PSI
(i.e., 11.07 PSI). That is, the intercepted ball
should have measured between 10.87 PSI and
11.07 PSI in the low-end case.
If one accepts the high end of the range implied
in the Wells report—that the Patriots balls had
been deflated by about 1.0 PSI—then the
intercepted ball should have measured between
11.32 PSI – 1 PSI (i.e., 10.32 PSI) and 11.52 PSI −
1 PSI (i.e., 10.52 PSI). That is, the intercepted ball
should have measured between 10.32 PSI and
10.52 PSI in the high-end case. The standard
deviation of the Patriots balls reported at halftime
was about 0.4. This means that the average of the
measurements, 11.52, is approximately 1 standard
deviation above the pressure that the Wells report
analysis would predict in the low-end case and
approximately 3 standard deviations above the
pressure that the Wells report analysis would
predict in the high-end case. If one were to
assume the facts presented in the Wells report to
be correct, then the odds of observing the
pressure reported by the Colts are about 1 out of 3
in the low-end case and less than 1 in 300 in the
high-end case—that is, quite unlikely.
Summary of Findings
The evidence we present points to a simple—and
innocent—explanation for the change in pressure
in the Patriots footballs. The Patriots balls were
measured at the start of halftime, whereas the
Colts balls were measured at the end of halftime,
after sufficient time had passed for the balls to
warm up and return to their pregame pressure.
There is no need to consider the alternative
average pressure drop of the Colts balls by 0.45 to 1.02 PSI, depending on various assumptions regarding the gauges used.”
A M E RI C A N E N TE R P R I S E IN S T I T U TE 1 1
hypothesis—that the Colts illegally inflated their
footballs—because a simple physical explanation
is available.
The fact that the average pressure of the Colts
balls was significantly above the prediction of the
Ideal Gas Law, while that of the Patriots balls was
not, is inconsistent with the findings of the Wells
report. Our conclusion that the warming of the
balls during halftime is the key factor overlooked
in the Wells report is supported by the
observation that the readings of the intercepted
Patriots football, measured separately from the
other Patriots balls, came in almost precisely at
the prediction of the law. Under the hypothesis
asserted by the Well report, the odds of this
Patriots ball matching the Ideal Gas Law
prediction were between 1 out of 3 and 1 out of
300. It is therefore unlikely that the Patriots
deflated the footballs.
About the Authors
Kevin A. Hassett is director of economic studies
and the State Farm James Q. Wilson Chair in
American Politics and Culture, Joseph W.
Sullivan is a research assistant, and Stan A.
Veuger is a resident scholar, all at AEI.
References
Boston Globe. 2015. “Full Transcript of Ted Wells’s
Conference Call on Deflategate Report.” May 12.
www.bostonglobe.com/sports/2015/05/12/full-
transcript-ted-wells-conference-call-deflategate-
report/sweK5ADLDyhQjnaVBmJRtM/story.html.
CBS Boston. 2015. “NFLPA’s DeMaurice Smith Rips
Credibility of Roger Goodell, Wells Report.” May 22.
http://boston.cbslocal.com/2015/05/22/nflpas-
demaurice-smith-rips-credibility-of-roger-goodell-
wells-report/.
Jones, Lindsay H. 2015. “Owner Robert Kraft Won’t
Appeal Patriots’ Deflategate Penalties.” USA Today,
May 19.
www.usatoday.com/story/sports/nfl/patriots/2015/
05/19/robert- kraft-deflategate-no-appeal-roger-
goodell-fine-draft-picks-new-england/27583829/.
Wells Jr., Theodore, Brad S. Karp, and Lorin L. Reisner.
2015. Investigative Report Concerning Footballs
Used During the AFC Championship Game on
January 18, 2015. Paul, Weiss, Rifkind, Wharton &
Garrison LLP, May 6.
http://nline.wsj.com/public/resources/document/D
eflategate.pdfhttp://nline.wsj.com/public/resources
/documents/Deflategate.pdf.
Arthur C. Brooks, President; Kevin A. Hassett,
Director of Economic Policy Studies; Michael R.
Strain, Deputy Director of Economic Policy Studies;
Stan Veuger, Editor, AEI Economic Perspectives
AEI Economic Perspectives is a publication of the
American Enterprise Institute for Public Policy
Research (AEI), a nonpartisan, not-for-profit,
501(c)(3) educational organization. The views
expressed in AEI publications are those of the
authors. AEI does not take institutional positions on
any issues.
© 2015 by the American Enterprise Institute for
Public Research. All rights reserved. For more
information on AEI Economic Perspectives, please
visit www.aei.org/feature/aei-economic-
perspectives/.
A M E RI C A N E N TE R P R I S E IN S T I T U TE 1 2
Appendix I
Assumptions regarding which gauge was used
before the game can have consequences for the
outcomes of subsequent analysis. For this reason,
when preparing data for our linear regression
analysis, we made additive or subtractive
adjustments of a factor of approximately 0.4 PSI
from the raw “unadjusted” values when
calculating the difference between the pregame
and halftime measurements.
Specifically, for ball k measured by gauge i, and
with values for HalftimePSI(k, i) extracted from the
halftime values reported in table 2 (“Pressure
measurements of the footballs as recorded on
Game Day”) in the Exponent section of the Wells
report, we started with the basic formula of
calculating the drop between the pregame
measurement period and halftime (Wells Jr.,
Karp, and Reisner 2015, 6):
PSI_dropk,i = PregamePSI(k, i) – HalftimePSI(k, i)
In cases in which, for the purposes of analyzing
all possible gauge permutations, we assumed that
ball k was measured by the high (Logo) gauge
before the game but measured by the low (Non-
Logo) gauge during halftime, we modified the
formula to be:
PSI_dropk,i = PregamePSI(k, high) – .4. - HalftimePSI(k, low)
The intuition behind this adjustment is
straightforward: the Wells report indicates that
the low gauge generates measurements that are
approximately 0.4 PSI lower than those of the
high gauge (Wells Jr., Karp, and Reisner 2015,
67). To benchmark the measurement obtained
from the low gauge at halftime against the
measurement obtained before the game with the
high gauge, therefore, one must adjust for the
measurement discrepancy between the two
gauges.
Given that the evidence in the Wells report
suggests that a scenario in which the low gauge
rather than the high gauge was used to generate
the pregame measurement would be one in which
the pregame measurement was approximately
0.4 PSI lower than a scenario in which the high
gauge was used to generate the pregame
measurement, a subtraction of 0.4 PSI from the
PregamePSI(k, high) term seems to be the appropriate
adjustment in cases in which the halftime
measurement is HalftimePSI(k, low).
We made the converse adjustment in cases in
which, for the purposes of analyzing all possible
gauge permutations, we assumed that ball k was
measured by the low gauge before the game, but
observed the measurement of the high gauge
during halftime. In such cases, we modified the
formula to be:
PSI_dropk,i = PregamePSI(k, low) + .4. - HalftimePSI(k, high)
The intuition behind this adjustment is, again,
straightforward: the Wells report indicates that
the high gauge generates measurements that are
approximately 0.4 PSI higher than those
generated by the low gauge. To benchmark the
measurement obtained from the high gauge at
halftime against the measurement obtained
before the game with the low gauge, therefore,
one must adjust for this measurement
discrepancy between the two gauges.
Given that the evidence in the Wells report
suggests that a scenario in which the high gauge
rather than the low gauge was used to generate
the pregame measurement would be one in which
the pregame measurement was approximately
0.4 PSI higher than a scenario in which the low
gauge was used to generate the pregame
measurement, an addition of 0.4 PSI from the
PregamePSI(k, low) term seems to be the appropriate
adjustment in which the halftime measurement is
HalftimePSI(k, high).
Tables A1–A4 present the data used in the linear
regressions. The unadjusted PSI drop values are a
simple difference of the starting PSI assumption
and the observed halftime PSI; the adjusted
values take into account the 0.4 difference, per
the methodology just described.
A M E RI C A N E N TE R P R I S E IN S T I T U TE 1 3
Table A1. Assuming Both Teams Start with the High Gauge
Team Order Ball
Pregame
Gauge
Halftime
Gauge
Starting
PSI
Halftime
PSI
PSI Drop
(Unadjusted)
PSI Drop
(Adjusted)
Patriots 1 P1 High Low 12.5 11.5 1 0.6
Patriots 2 P2 High Low 12.5 10.85 1.65 1.25
Patriots 3 P3 High Low 12.5 11.15 1.35 0.95
Patriots 4 P4 High Low 12.5 10.7 1.8 1.4
Patriots 5 P5 High Low 12.5 11.1 1.4 1
Patriots 6 P6 High Low 12.5 11.6 0.9 0.5
Patriots 7 P7 High Low 12.5 11.85 0.65 0.25
Patriots 8 P8 High Low 12.5 11.1 1.4 1
Patriots 9 P9 High Low 12.5 10.95 1.55 1.15
Patriots 10 P10 High Low 12.5 10.5 2 1.6
Patriots 11 P11 High Low 12.5 10.9 1.6 1.2
Patriots 1 P1 High High 12.5 11.8 0.7 0.7
Patriots 2 P2 High High 12.5 11.2 1.3 1.3
Patriots 3 P3 High High 12.5 11.5 1 1
Patriots 4 P4 High High 12.5 11 1.5 1.5
Patriots 5 P5 High High 12.5 11.45 1.05 1.05
Patriots 6 P6 High High 12.5 11.95 0.55 0.55
Patriots 7 P7 High High 12.5 12.3 0.2 0.2
Patriots 8 P8 High High 12.5 11.55 0.95 0.95
Patriots 9 P9 High High 12.5 11.35 1.15 1.15
Patriots 10 P10 High High 12.5 10.9 1.6 1.6
Patriots 11 P11 High High 12.5 11.35 1.15 1.15
Colts 12 C1 High High 13.1 12.7 0.4 0.4
Colts 13 C2 High High 13.1 12.75 0.35 0.35
Colts 14 C3 High High 13.1 12.5 0.6 0.6
Colts 15 C4 High High 13.1 12.55 0.55 0.55
Colts 12 C1 High Low 13.1 12.35 0.75 0.35
Colts 13 C2 High Low 13.1 12.3 0.8 0.4
Colts 14 C3 High Low 13.1 12.95 0.15 -0.25
Colts 15 C4 High Low 13.1 12.15 0.95 0.55
A M E RI C A N E N TE R P R I S E IN S T I T U TE 1 4
Table A2. Assuming Only the Patriots Start with the High Gauge
Team Order Ball
Pregame
Gauge
Halftime
Gauge
Starting
PSI
Halftime
PSI
PSI Drop
(Unadjusted)
PSI Drop
(Adjusted)
Patriots 1 P1 High Low 12.5 11.5 1 0.6
Patriots 2 P2 High Low 12.5 10.85 1.65 1.25
Patriots 3 P3 High Low 12.5 11.15 1.35 0.95
Patriots 4 P4 High Low 12.5 10.7 1.8 1.4
Patriots 5 P5 High Low 12.5 11.1 1.4 1
Patriots 6 P6 High Low 12.5 11.6 0.9 0.5
Patriots 7 P7 High Low 12.5 11.85 0.65 0.25
Patriots 8 P8 High Low 12.5 11.1 1.4 1
Patriots 9 P9 High Low 12.5 10.95 1.55 1.15
Patriots 10 P10 High Low 12.5 10.5 2 1.6
Patriots 11 P11 High Low 12.5 10.9 1.6 1.2
Patriots 1 P1 High High 12.5 11.8 0.7 0.7
Patriots 2 P2 High High 12.5 11.2 1.3 1.3
Patriots 3 P3 High High 12.5 11.5 1 1
Patriots 4 P4 High High 12.5 11 1.5 1.5
Patriots 5 P5 High High 12.5 11.45 1.05 1.05
Patriots 6 P6 High High 12.5 11.95 0.55 0.55
Patriots 7 P7 High High 12.5 12.3 0.2 0.2
Patriots 8 P8 High High 12.5 11.55 0.95 0.95
Patriots 9 P9 High High 12.5 11.35 1.15 1.15
Patriots 10 P10 High High 12.5 10.9 1.6 1.6
Patriots 11 P11 High High 12.5 11.35 1.15 1.15
Colts 12 C1 Low High 13.1 12.7 0.4 0.8
Colts 13 C2 Low High 13.1 12.75 0.35 0.75
Colts 14 C3 Low High 13.1 12.5 0.6 1
Colts 15 C4 Low High 13.1 12.55 0.55 0.95
Colts 12 C1 Low Low 13.1 12.35 0.75 0.75
Colts 13 C2 Low Low 13.1 12.3 0.8 0.8
Colts 14 C3 Low Low 13.1 12.95 0.15 0.15
Colts 15 C4 Low Low 13.1 12.15 0.95 0.95
A M E RI C A N E N TE R P R I S E IN S T I T U TE 1 5
Table A3. Assuming Only the Colts Start with the High Gauge
Team Order Ball
Pregame
Gauge
Halftime
Gauge
Starting
PSI
Halftime
PSI
PSI Drop
(Unadjusted)
PSI Drop
(Adjusted)
Patriots 1 P1 Low Low 12.5 11.5 1 1
Patriots 2 P2 Low Low 12.5 10.85 1.65 1.65
Patriots 3 P3 Low Low 12.5 11.15 1.35 1.35
Patriots 4 P4 Low Low 12.5 10.7 1.8 1.8
Patriots 5 P5 Low Low 12.5 11.1 1.4 1.4
Patriots 6 P6 Low Low 12.5 11.6 0.9 0.9
Patriots 7 P7 Low Low 12.5 11.85 0.65 0.65
Patriots 8 P8 Low Low 12.5 11.1 1.4 1.4
Patriots 9 P9 Low Low 12.5 10.95 1.55 1.55
Patriots 10 P10 Low Low 12.5 10.5 2 2
Patriots 11 P11 Low Low 12.5 10.9 1.6 1.6
Patriots 1 P1 Low High 12.5 11.8 0.7 1.1
Patriots 2 P2 Low High 12.5 11.2 1.3 1.7
Patriots 3 P3 Low High 12.5 11.5 1 1.4
Patriots 4 P4 Low High 12.5 11 1.5 1.9
Patriots 5 P5 Low High 12.5 11.45 1.05 1.45
Patriots 6 P6 Low High 12.5 11.95 0.55 0.95
Patriots 7 P7 Low High 12.5 12.3 0.2 0.6
Patriots 8 P8 Low High 12.5 11.55 0.95 1.35
Patriots 9 P9 Low High 12.5 11.35 1.15 1.55
Patriots 10 P10 Low High 12.5 10.9 1.6 2
Patriots 11 P11 Low High 12.5 11.35 1.15 1.55
Colts 12 C1 High High 13.1 12.7 0.4 0.4
Colts 13 C2 High High 13.1 12.75 0.35 0.35
Colts 14 C3 High High 13.1 12.5 0.6 0.6
Colts 15 C4 High High 13.1 12.55 0.55 0.55
Colts 12 C1 High Low 13.1 12.35 0.75 0.35
Colts 13 C2 High Low 13.1 12.3 0.8 0.4
Colts 14 C3 High Low 13.1 12.95 0.15 -0.25
Colts 15 C4 High Low 13.1 12.15 0.95 0.55
A M E RI C A N E N TE R P R I S E IN S T I T U TE 1 6
Table A4: Assuming Both Teams Start with the Low Gauge
Team Order Ball
Pregame
Gauge
Halftime
Gauge
Starting
PSI
Halftime
PSI
PSI Drop
Unadjusted
PSI Drop
Adjusted
Patriots 1 P1 Low Low 12.5 11.5 1 1
Patriots 2 P2 Low Low 12.5 10.85 1.65 1.65
Patriots 3 P3 Low Low 12.5 11.15 1.35 1.35
Patriots 4 P4 Low Low 12.5 10.7 1.8 1.8
Patriots 5 P5 Low Low 12.5 11.1 1.4 1.4
Patriots 6 P6 Low Low 12.5 11.6 0.9 0.9
Patriots 7 P7 Low Low 12.5 11.85 0.65 0.65
Patriots 8 P8 Low Low 12.5 11.1 1.4 1.4
Patriots 9 P9 Low Low 12.5 10.95 1.55 1.55
Patriots 10 P10 Low Low 12.5 10.5 2 2
Patriots 11 P11 Low Low 12.5 10.9 1.6 1.6
Patriots 1 P1 Low High 12.5 11.8 0.7 1.1
Patriots 2 P2 Low High 12.5 11.2 1.3 1.7
Patriots 3 P3 Low High 12.5 11.5 1 1.4
Patriots 4 P4 Low High 12.5 11 1.5 1.9
Patriots 5 P5 Low High 12.5 11.45 1.05 1.45
Patriots 6 P6 Low High 12.5 11.95 0.55 0.95
Patriots 7 P7 Low High 12.5 12.3 0.2 0.6
Patriots 8 P8 Low High 12.5 11.55 0.95 1.35
Patriots 9 P9 Low High 12.5 11.35 1.15 1.55
Patriots 10 P10 Low High 12.5 10.9 1.6 2
Patriots 11 P11 Low High 12.5 11.35 1.15 1.55
Colts 12 C1 Low High 13.1 12.7 0.4 0.8
Colts 13 C2 Low High 13.1 12.75 0.35 0.75
Colts 14 C3 Low High 13.1 12.5 0.6 1
Colts 15 C4 Low High 13.1 12.55 0.55 0.95
Colts 12 C1 Low Low 13.1 12.35 0.75 0.75
Colts 13 C2 Low Low 13.1 12.3 0.8 0.8
Colts 14 C3 Low Low 13.1 12.95 0.15 0.15
Colts 15 C4 Low Low 13.1 12.15 0.95 0.95